InterviewSolution
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InterviewSolution
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Statement 1 If one root of `Ax^(3)+Bx^(2)+Cx+D=0 A!=0`, is the arithmetic mean of the other two roots, then the relation `2B^(3)+k_(1)ABC+k_(2)A^(2)D=0` holds good and then `(k_(2)-k_(1))` is a perfect square. Statement -2 If a,b,c are in AP then `b` is the arithmetic mean of a and c.A. Statement -1 is true, Statement -2 is true, Statement -2 is a correct explanation for Statement-1B. Statement -1 is true, Statement -2 is true, Statement -2 is not a correct explanation for Statement -1C. Statement -1 is true, Statement -2 is falseD. Statement -1 is false, Statement -2 is true |
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Answer» Correct Answer - A Let roots of `Ax^(3)+Bx^(2)+Cx+D=0`……….i are `alpha-beta, alpha, alpha+beta` (in AP) Then `(alpha-beta)+alpha+(alpha+beta)=-B/A` `impliesalpha=-B/(3A)`, which is a root of Eq. (i) Then `A alpha^(3)+B alpha^(2)+C alpha +D=0` `impliesA(-B/(3A))^(3)+B(-B/(3A))^(2)+C(-B/(3A))+D=0` `implies-(B^(3))/(27A^(2))+(B^(3))/(9A^(2))-(BC)/(3A)+D=0` `implies2B^(3)-9ABC+27A^(2)D=0` Now comparing with `2B^(3)+k_(1)ABC+k_(2)A^(2)D=0` we get `k_(1)=-9,k_(2)=27` `:.k_(2)-k_(1)=27-(-9)=36=6^(2)` Hence both statement are true and Statement 2 is a correct explanation of Statement -1. |
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